This paper predicts the lower-bound shakedown limit of an elastoplastic half-space under traffic loads based on the first dynamic shakedown theory. A three-dimensional finite element model with infinite element boundaries is built. And then the model is used to analyze the dynamic elastic stress under different speed moving loads, and a steady residual stress field is constructed through the dynamic elastic stress. A method to predict the dynamic shakedown limits through analyzing the residual stress is proposed as well. Then the lower-bound shakedown limits of half-space under dynamic traffic load and the influence of speed on shakedown limits are discussed. Meanwhile, the difference of shakedown limits between uniform load and Hertz load are studied. In addition, the shakedown limits will increase with the growth of moving speed when the load speed is lower than Rayleigh wave speed, otherwise the shakedown limits will decrease with the growth of moving speed when the load speed is faster than Rayleigh wave speed. It is also found that shakedown limits of uniform load and Hertz load are similar when the total weight load of this two load manners are the same.